Short of a school textbook or a book which contains the things you said you dislike, I don’t think you’ll find too many good single-volume US history books out there.
“A People’s History of the United States” is good for including some things I had never seen before, at least until college, but Howard Zinn isn’t exactly objective and definitely takes out a lot of context and even historical facts when trying to make US history fit into his worldview.
Instead, you may just want to look at a US history chronology and pick out various eras and events which you are interested in or know little about. Jeff Shaara writes pretty decent historical fiction of the Revolutionary war, civil war, Mexican-American war, and WWI. If you have the interest in US history and most importantly the time, you probably want to take this approach anyway since any single-volume history is bound to leave a lot out and won’t always give you a full understanding of how and why something happened - or didn’t.